The Complete Aristotle (eng.)

and
reason would be obvious simultaneously. For the act of perception
would have enabled us to know the universal too; since, the present
fact of an eclipse being evident, perception would then at the same
time give us the present fact of the earth’s screening the sun’s
light, and from this would arise the universal.
    Thus, as we maintain, to know a thing’s nature is to know the
reason why it is; and this is equally true of things in so far as
they are said without qualification to he as opposed to being
possessed of some attribute, and in so far as they are said to be
possessed of some attribute such as equal to right angles, or
greater or less.
3
    It is clear, then, that all questions are a search for a
‘middle’. Let us now state how essential nature is revealed and in
what way it can be reduced to demonstration; what definition is,
and what things are definable. And let us first discuss certain
difficulties which these questions raise, beginning what we have to
say with a point most intimately connected with our immediately
preceding remarks, namely the doubt that might be felt as to
whether or not it is possible to know the same thing in the same
relation, both by definition and by demonstration. It might, I
mean, be urged that definition is held to concern essential nature
and is in every case universal and affirmative; whereas, on the
other hand, some conclusions are negative and some are not
universal; e.g. all in the second figure are negative, none in the
third are universal. And again, not even all affirmative
conclusions in the first figure are definable, e.g. ‘every triangle
has its angles equal to two right angles’. An argument proving this
difference between demonstration and definition is that to have
scientific knowledge of the demonstrable is identical with
possessing a demonstration of it: hence if demonstration of such
conclusions as these is possible, there clearly cannot also be
definition of them. If there could, one might know such a
conclusion also in virtue of its definition without possessing the
demonstration of it; for there is nothing to stop our having the
one without the other.
    Induction too will sufficiently convince us of this difference;
for never yet by defining anything-essential attribute or
accident-did we get knowledge of it. Again, if to define is to
acquire knowledge of a substance, at any rate such attributes are
not substances.
    It is evident, then, that not everything demonstrable can be
defined. What then? Can everything definable be demonstrated, or
not? There is one of our previous arguments which covers this too.
Of a single thing qua single there is a single scientific
knowledge. Hence, since to know the demonstrable scientifically is
to possess the demonstration of it, an impossible consequence will
follow:-possession of its definition without its demonstration will
give knowledge of the demonstrable.
    Moreover, the basic premisses of demonstrations are definitions,
and it has already been shown that these will be found
indemonstrable; either the basic premisses will be demonstrable and
will depend on prior premisses, and the regress will be endless; or
the primary truths will be indemonstrable definitions.
    But if the definable and the demonstrable are not wholly the
same, may they yet be partially the same? Or is that impossible,
because there can be no demonstration of the definable? There can
be none, because definition is of the essential nature or being of
something, and all demonstrations evidently posit and assume the
essential nature-mathematical demonstrations, for example, the
nature of unity and the odd, and all the other sciences likewise.
Moreover, every demonstration proves a predicate of a subject as
attaching or as not attaching to it, but in definition one thing is
not predicated of another; we do not, e.g. predicate animal of
biped nor biped of animal, nor yet figure of plane-plane not being
figure nor figure plane. Again, to prove essential nature is not
the same as to prove the fact of a connexion. Now definition
reveals essential nature, demonstration reveals that a given
attribute attaches or does not attach to a given subject; but
different things require different demonstrations-unless the one
demonstration is related to the other as part to whole. I add this
because if all triangles have been proved to possess angles equal
to two right angles, then this attribute has been proved to attach
to isosceles; for isosceles is a part